<p>I can't figure out why the correct answer to this is B. It seems to me B and E could both be correct. With B, the total length of PQR is 21 and the length of STU could also be 21 with each side being length 7.</p>
<p>
In triangle PQR sides PQ and QR have lengths 5 and 11 respectively. Triangle PQR has the same perimeter as equilateral triangle STU. If the length of side ST is an integer, which of the following could be the length of side PR</p>
<p>A. 15
B. 14
C. 10
D. 9
E. 5
</p>
<p>E doesn’t work because you can’t make a triangle with side lengths 5, 5, and 11. For a triangle, every side length has to be less then the sum of the other two. Its like trying to make a triangle with two toothpicks and a meter stick. 5 and 5 are too short to be with an 11</p>
<p>By the triangle inequality rule, side PR must be greater than the difference of the other two sides but less than the sum.</p>
<p>6 < x < 16</p>
<p>Therefore, E cannot be the answer.</p>
<p>Consider the two conditions:
<p>The only two numbers that fulfill the first condition are 14 (B) and 5 (E).
However, only answer choice B fulfills the AND of condition number 2.</p>
<p>The answer, t.f., is B. ^__^</p>